Interactive and Intuitive Physics-based Blending Surface Design for the Second Order Algebraic Implicit Surfaces

  • 발행 : 2009.06.30

초록

We present a physics-based blending method for the second order algebraic implicit surface. Unlike other traditional blending techniques, the proposed method avoids complex mathematical operations and unwanted artifacts like bulge, which have highly limited the application of the second order algebraic implicit surface as a modeling primitive in spite of lots of its excellent properties. Instead, the proposed method provides the designer with flexibility to control the shapes of the blending surface on interactive basis; the designer can check and design the shape of blending surfaces accurately by simply adjusting several physics parameter in real time, which was impossible in the traditional blending methods. In the later parts of this paper, several results are also presented.

키워드

참고문헌

  1. James F. Blinn, "A Generalization of Algebraic Surface Drawing," ACM Transactions on Graphics, Vol.1, No.3, pp. 235-356, 1982. https://doi.org/10.1145/357306.357310
  2. William J Schroeder, William E. Lorensen, and Steve Linthicum, "Implicit Modeling of Swept Surfaces and Volumes," Proceedings of the conference on Visualization '94, pp. 40-45, 1994.
  3. Antoine Leclercq, S. Akkouche, and E. Galin, "Mixing Triangle Meshes and Implicit Surfaces in Character Animation," Proceedings of the Eurographic Workshop on Computer Animation and Simulation, pp. 37-47, 2001.
  4. W.H. Press, S. A. Teukolsky, W.T. Vetterling, and B. P. Flannery, Numerical Recipes in C: The Art of Scientific Computing, 2nd edition, Cambridge University Press, Cambridge, pp. 120-122, 1993.
  5. Masatoshi Matsumiya, Haruo Takemura, and Naokazu Yokoya, "An Immersive Modeling System for 3D Free-form Design Using Implicit Surfaces," Proceedings of the ACM symposium on Virtual reality software and technology, pp. 67-74 , 2000.
  6. Jing Hua and Hong Qin, "Dynamic Implicit Solids with Constraints for Haptic Sculpting," Proceedings of the Shape Modeling International 2002, pp. 119-129, 2002.
  7. Geoff Wyvill, Introduction to Implicit Surfaces, Morgan Kaufmann Publishers, Inc., San Francisco, CA, 1997.
  8. William E. Lorensen and Harvey E. Cline, "International Conference on Computer Graphics and Interactive Techniques," Proceedings of the 14th annual conference on Computer graphics and interactive techniques, pp. 163-169, 1987.
  9. Barton T. Stander and John C. Hart, "Guaranteeing the Topology of an Implicit Surface Polygonization for Interactive Modeling," Proceedings of the 24th annual conference on Computer graphics and interactive techniques, pp. 279-286, 1997.
  10. John C. Hart, "Morse Theory for Implicit Surface Modeling," Proceedings of Visualization and Mathematics, pp. 257-268, 1997.
  11. John M. Snyder, "Interval Analysis for Computer Graphics," Proceedings of the 19th annual conference on Computer graphics and interactive techniques, pp. 121-130, 1992.
  12. Yutaka Ohtake and Alexander G. Belyaev, "Dual/Primal Mesh Optimization for Polygonized Implicit Surfaces," Proceedings of the seventh ACM Symposium on Solid Modeling and Applications, pp. 171-178, 2002.
  13. M. Desbrun, N. Tsingos, and M.-P. Gascuel, "Adaptive Sampling of Implicit Surfaces for Interactive Modeling and Animation," Proceedings of Implicit Surface '95, Vol.15, No.5, pp. 319-325, 1995.
  14. B. Crespin, P. Guitton, and C. Schlick. "Efficient and Accurate Tessellation of Implicit Sweep Objects," Proceedings of Constructive Solid Geometry '98, 1998.
  15. Andrew P. Witkin and Paul S. Heckbert, "Using Particles to Sample and Control Implicit Surfaces," Proceedings of the 21st annual conference on Computer graphics and interactive techniques, pp. 269-277, 1994.
  16. John Woodwark, "Blends in Geometric Modeling," Proceedings on Mathematics of Surfaces II, pp. 255-297, 1987
  17. Alyn Rockwood, Introduction to Implicit Surfaces, Morgan Kaufmann Publishers, Inc., San Francisco, CA, 1997.
  18. Christoph Hoffmann and John Hopcroft, The Potential Method for Blending Surfaces and Corners, Geometric Modeling, SIAM Publications, Philadelphia, 1987.
  19. Menno Kosters, "An Extension of the Potential Method to Higher-Order Blendings," Proceedings of the first ACM symposium on Solid modeling foundations and CAD/CAM applications, pp. 329-337, 1991.
  20. Jules Bloomenthal and Brian Wyvill, "Interactive Techniques for Implicit Modeling," Symposium on Interactive 3D Graphics, Vol.24, No.2, pp. 109-116, 1990.
  21. Anil Kaul and Jarek Rossignac, "Solid- interpolation deformations: Construction and animation of pips," Proceedings of EUROGRAPHICS '91 (Sept.), pp. 493-505, 1991.
  22. Andrei Sherstyuk, "Interactive Shape Design with Convolution Surfaces," Proceedings of the International Conference on Shape Modeling and Applications, pp. 56-65, 1999.
  23. Laurent Hilde, Philippe Meseure, and Christophe Chailou, "A Fast Implicit Integration Method for Solving Dynamic Equations of Movement," Proceedings of the ACM symposium on Virtual reality software and technology, pp. 71-76, 2001.
  24. David M. Bourg, Physics for Game Developers, 1st ed., O'Reilly & Associates, Inc., Sebastopol, CA, 2002.
  25. Kwang-jin Choi and Hyeong-seok Ko, "Stable but Responsive Cloth," ACM Transactions on Graphics, SIGGRAPH 2002, Vol.21, No.3, pp. 604-611, 2002.
  26. D. Baraff and A. Witkin, "Large Steps in Cloth Simulation," Proceedings of the 25th annual conference on Computer graphics and interactive techniques, pp. 43-54, 1998.
  27. H. Hoppe, "Progressive Meshes," Proceedings of the 23rd annual conference on Computer graphics and interactive techniques, pp. 99-108, 1996.